Sphere

Steve Kline 06 NOV 1998

Alan Munter 08 JULY 1999, converted to Java

Calculates the form factor, P(q), for a monodisperse spherical particle with uniform scattering length density. The form factor is normalized by the particle volume as described below.

Resolution smeared version is also provided.

Input Variables (default values):

Parameter	Variable	Value
0	Scale	1.0
1	Radius (Å)	60.0
2	Contrast (Å-2)	1.0e-6
3	Incoherent Background (cm-1)	0.0

The function calculated is:

The returned value is scaled to units of [cm^-1]

Scattering contrast (Dr) = SLD (core) - SLD (solvent)

Parameter[0] (scale) and Parameter[2] (contrast) are both multiplicative factors in the model and are perfectly correlated. One or both of these parameters must be held fixed during model fitting.

If the scale factor Parameter[0] is set equal to the particle volume fraction, phi, then the returned value is the scattered intensity per unit volume, I(q) = phi*P(q). However, no interparticle interference effects are included in this calculation.

Guinier, A. and G. Fournet, "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York, (1955).

This example dataset is produced by calculating the Sphere using 128 data points, q_min = 0.001 Å^-1, q_max = 0.3 (Å^-1) and the above default parameter values.